Is it possible to generate "Karel the robot" programs with genetic programming?
A genetic algorithm is used to find an optimal solution to a problem. The parameters of the problem are encoded in the population, where each individual contains a solution to the problem in itself. Each individual is evaluated using a fitness function, and then the highest scoring individuals are used to create a new set of individuals by mixing up their parameters, and this new set replaces the worst scoring individuals from the previous generation. Over time, the average fitness of the population will (hopefully) increase, and a good solution be found. Essentially, the search space is explored in parallel through the many individuals in the population, which means that local maxima can probably be avoided.

The question now is: What is the problem you want to optimise?

The Karel language is fairly simple, and has few tokens. A program should be easily encodable in the right format, though genetic algorithms usually require individuals to have the same size (though shorter programs could be padded with no-ops). Recombining the best programs could mean swapping tokens. Maybe syntactic constraints could be factored into this to avoid crass syntactic errors. That should not be an insurmountable problem.

However, that still leaves the question of the fitness function. A basic criterion would be syntactic: if the program doesn't parse, it's not 'fit'. This could potentially wipe out a lot of offspring, and doesn't really help you much: it would produce more or less random programs which are syntactically well-formed.

What you really want is to evaluate the outcome of the programs. Like, which program can best navigate a maze. So you need to execute them and see what they produce. Then you run straight away into the halting problem: your little program might contain an endless loop and will never terminate. So you need to add a kind of time-out, or a limit on the steps the program can execute. This should be easy to do in a virtual machine.

So, to answer your question: Yes, it is possible to turn creating Karel programs into a problem that a genetic algorithm can be applied to. However, you need to be clear about what problem you want to solve. I don't quite understand what you mean by "learning from demonstration" or how you can achieve the aim of replicating human actions, but if you can somehow encode that in a fitness function, GAs are a tool you can use.